球形粒子之塗佈對抗反射膜抗反射效率的影響

Abstract

本文主要討論的是單層球形粒子塗佈在基板上所呈現的抗反射效應可以利用已知的理論來分析結果。被鍍在基板上的球形粒子可以視為由很多層具有不同折射率的膜層所建構而成，且球形粒子具有幾何對稱以漸變式的折射率改變方式存在整個架構中。反射率的大小可以透過抗反射膜理論中的膜矩陣理論計算得到。數值模擬中的球形粒子材料可以是由二氧化矽以及二氧化鈦以不同比例混合而得，或是其他合適的高分子混合而得，常見的例子有聚苯乙烯。實際上反射率以及穿透率是會隨著不同的粒子折射率以及基板折射率而有所不同，其中粒子之間的距離以及相對大小的改變也會是影響反射率大小的極大變因。結果顯示出當粒子半徑為40奈米，排列的方式以四方緊密之堆積排列而成而且具有折射率為1.35時，反射率在波長為389奈米存在最小值可到0.0068%。使用嚴格耦合波理論(rigorous coupled wave analysis，RCWA)以及等效折射率理論(effective medium theory)計算粒子半徑是40奈米時的狀況卻只有在往長波長的時候才有相近的趨勢。造成此現象的原因可能是因為粒子排列的週期與入射波長的差距還不夠大，以及使用RCWA求反射率時所給的和諧數(harmonics)太少導致解微分方程式出現了部份誤差。

The anti-reflective behavior of a layer of mono-dispersed spherical particles coated onto a substrate is analyzed theoretically. The coated particles are divided into multiple layers each plays the role of a film, and the overall reflectivity is estimated by the anti-reflective theorem for a single film. Numerical simulations are conducted in which the particle material is SiO2 mixed with TiO2 or appropriate polymers such as polystyrene. We show that both the reflectivity and the transmittivity of the system vary with the refractive index of the particle and that of substrate. For particles of radius 40 nm and refractive index 1.35, the reflectivity has the minimum value of 0.0068 % at 389 nm. The results of reflectance by RCWA and EMT in the case of particles of radius 40 nm, refractive index 1.46 have similar tendency on visible wavelength. The reasons of inaccuracy are possible for that when the period of spherical particles is not enough smaller than incident wavelength, and we work out differential equations, harmonics is insufficient.